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Maximum nash welfare and other stories about EFX

Amanatidis, G and Birmpas, G and Filos-Ratsikas, A and Hollender, A and Voudouris, AA (2020) Maximum nash welfare and other stories about EFX. In: UNSPECIFIED, ? - ?.

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Abstract

We consider the classic problem of fairly allocating indivisible goods among agents with additive valuation functions and explore the connection between two prominent fairness notions: maximum Nash welfare (MNW) and envy-freeness up to any good (EFX). We establish that an MNW allocation is always EFX as long as there are at most two possible values for the goods, whereas this implication is no longer true for three or more distinct values. As a notable consequence, this proves the existence of EFX allocations for these restricted valuation functions. While the efficient computation of an MNW allocation for two possible values remains an open problem, we present a novel algorithm for directly constructing EFX allocations in this setting. Finally, we study the question of whether an MNW allocation implies any EFX guarantee for general additive valuation functions under a natural new interpretation of approximate EFX allocations.

Item Type: Conference or Workshop Item (UNSPECIFIED)
Additional Information: Published proceedings: IJCAI International Joint Conference on Artificial Intelligence
Divisions: Faculty of Science and Health > Computer Science and Electronic Engineering, School of
Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: Elements
Date Deposited: 15 Apr 2020 15:30
Last Modified: 31 Mar 2021 08:15
URI: http://repository.essex.ac.uk/id/eprint/27298

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